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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Improving ADAM through an implicit-explicit (IMEX) time-stepping approach

The ADAM optimizer, often used in machine learning for neural network training, corresponds to an underlying ordinary differential equation (ODE) in the limit of very small learning rates. Here, this work shows that the classical ADAM algorithm is a first-order implicit-explicit (IMEX) Euler discretization of the underlying ODE. Employing the time discretization point of view, we propose new extensions of the ADAM scheme obtained by using higher-order IMEX methods to solve the ODE. Based on this approach, we derive a new optimization algorithm for neural network training that performs better than classical ADAM on several regression and classification problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2007

Comparison of Fixed and Variable Time Step Trajectory Integration Methods for Cislunar Trajectories

Due to the nonlinear nature of the Earth-Moon-Sun three-body problem and non-spherical gravity, CEV cislunar targeting algorithms will require many propagations in their search for a desired trajectory. For on-board targeting especially, the algorithm must have a simple, fast, and accurate propagator to calculate a trajectory with reasonable computation time, and still be robust enough to remain stable in the various flight regimes that the CEV will experience. This paper compares Cowell s method with a fourth-order Runge- Kutta integrator (RK4), Encke s method with a fourth-order Runge-Kutta- Nystr m integrator (RKN4), and a method known as Multi-Conic. Additionally, the study includes the Bond-Gottlieb 14-element method (BG14) and extends the investigation of Encke-Nystrom methods to integrators of higher order and with variable step size.

Weeks, ichael W.↗
NASA NTRS1988

Parametric study of grid size, time step and turbulence modeling on Navier-Stokes computations over airfoils

An upwind-biased implicit approximate factorization algorithm is applied to several steady and unsteady turbulent flows. The thin layer form of the compressible Navier-Stokes equation is used. Both the flux vector splitting and flux difference splitting methods are used to determine fluxes, and the results are compared. Flux difference splitting predicts results more accurately than flux vector splitting on a given mesh size, but, in its present implementation, is more severely limited by the maximum CFL number for unsteady time accurate flows. Physical aspects of the computations are also examined. An equilibrium turbulent boundary layer model computes generally better steady and unsteady results than a nonequilibrium model when there is little to no boundary layer separation. Conversely, when a significant region of separation exists, the nonequilibrium model performs in better agreement with experiment.

Rumsey, Christopher L.↗
DOE OSTI2023

A Two-Step Time-Series Data Clustering Method for Building-Level Load Profile

Residential and commercial buildings have huge potential to contribute value to improve grid resilience by participating grid services. To reveal the significant value, it is critical to estimate the grid service capability from these buildings. Unlike the large-scale distributed energy resources such as wind and solar farms, those buildings need to participate grid services in aggregation, not by individual. Therefore, it is important to appropriately group buildings for aggregation. The load profiles in the same group will have similar characteristics at the same time step, so grid operators can send the grid service signal to the customer group with a higher chance to respond at that time step. In this paper, we develop a load profile clustering method to classify the building-level load profiles for grid service capability estimation. In our two-step clustering approach, we first calculate the total load consumption for each building, clustering the load profiles based on energy consumption level. Then, we further cluster the load profiles in each energy cluster based on the load shape. The parameter selection for each clustering step is discussed. The proposed method is applied on actual building-level load profiles, and the results have proved the effectiveness of this method.

advanced metering infrastructure (AMI)↗
DOE OSTI2023

A Two-Step Time-Series Data Clustering Method for Building-Level Load Profile

Residential and commercial buildings have huge potential to contribute value to improve grid resilience by participating grid services. To reveal the significant value, it is critical to estimate the grid service capability from these buildings. Unlike the large-scale distributed energy resources such as wind and solar farms, those buildings need to participate grid services in aggregation, not by individual. Therefore, it is important to appropriately group buildings for aggregation. The load profiles in the same group will have similar characteristics at the same time step, so grid operators can send the grid service signal to the customer group with a higher chance to respond at that time step. In this paper, we develop a load profile clustering method to classify the building-level load profiles for grid service capability estimation and the results have proved the effectiveness of this method.

AMI↗
NASA NTRS2006

Convergence Acceleration for Multistage Time-Stepping Schemes

The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 could be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. Numerical dissipation operators (based on the Roe scheme, a matrix formulation, and the CUSP scheme) as well as the number of RK stages are considered in evaluating the RK/implicit scheme. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. In two dimensions, turbulent flows over an airfoil at subsonic and transonic conditions are computed. The effects of mesh cell aspect ratio on convergence are investigated for Reynolds numbers between 5.7 x 10(exp 6) and 100.0 x 10(exp 6). Results are also obtained for a transonic wing flow. For both 2-D and 3-D problems, the computational time of a well-tuned standard RK scheme is reduced at least a factor of four.

Swanson, R. C.↗
NASA NTRS1986

On a large time-step high resolution scheme

This paper presents a class of new second-order accurate (2K + 3)-point explicit schemes for the computation of weak solutions of hyperbolic conservation laws, that are total-variation-diminishing under a Courant-Friedrichs-Lewy restriction of K. These highly nonlinear schemes are obtained by applying a nonoscillatory first-order accurate (2K + 1)-point scheme to a modified flux. The derived second-order accurate schemes achieve high resolutions, while retaining the robustness of the original first-order accurate scheme.

Harten, A.↗
NASA NTRS1991

Characteristic time-stepping or local preconditioning of the Euler equations

A derivation is presented of a local preconditioning matrix for multidimensional Euler equations, that reduces the spread of the characteristic speeds to the lowest attainable value. Numerical experiments with this preconditioning matrix are applied to an explicit upwind discretization of the two-dimensional Euler equations, showing that this matrix significantly increases the rate of convergence to a steady solution. It is predicted that local preconditioning will also simplify convergence-acceleration boundary procedures such as the Karni (1991) procedure for the far field and the Mazaheri and Roe (1991) procedure for a solid wall.

Van Leer, Bram↗
NASA NTRS1992

The impact of time step definition on code convergence and robustness

We have implemented preconditioning for multi-species reacting flows in two independent codes, an implicit (ADI) code developed in-house and the RPLUS code (developed at LeRC). The RPLUS code was modified to work on a four-stage Runge-Kutta scheme. The performance of both the codes was tested, and it was shown that preconditioning can improve convergence by a factor of two to a hundred depending on the problem. Our efforts are currently focused on evaluating the effect of chemical sources and on assessing how preconditioning may be applied to improve convergence and robustness in the calculation of reacting flows.

Venkateswaran, S.↗
NASA NTRS2011

Collocation and Galerkin Time-Stepping Methods

We study the numerical solutions of ordinary differential equations by one-step methods where the solution at tn is known and that at t(sub n+1) is to be calculated. The approaches employed are collocation, continuous Galerkin (CG) and discontinuous Galerkin (DG). Relations among these three approaches are established. A quadrature formula using s evaluation points is employed for the Galerkin formulations. We show that with such a quadrature, the CG method is identical to the collocation method using quadrature points as collocation points. Furthermore, if the quadrature formula is the right Radau one (including t(sub n+1)), then the DG and CG methods also become identical, and they reduce to the Radau IIA collocation method. In addition, we present a generalization of DG that yields a method identical to CG and collocation with arbitrary collocation points. Thus, the collocation, CG, and generalized DG methods are equivalent, and the latter two methods can be formulated using the differential instead of integral equation. Finally, all schemes discussed can be cast as s-stage implicit Runge-Kutta methods.

Huynh, H. T.↗